Apart from what has been mentioned already, you might consider using Bing Routing service that should be available in ArcGIS API for Javascript. I have personally seen the sample working with ArcGIS API for Silverlight though. The Bing Maps seems to cover India geographically, so the routing service should be available there even when accessing programmatically.

Some other alternatives are consuming the routing services from Nokia or TomTom (TomTom might not cover India though) with their APIs and then parsing and visualizing the response in JS API since it comes back what I've seen so far in JSON with the geometry and such.

If you will plan to build your own network analysis services, consider using OSM Planet, for example, available for download for free from http://market.weogeo.com. This will give you access to the roads in India you might use then in ArcGIS for building own network datasets.